Texas, the powerhouse of the death penalty in America which last year executed more than twice the number of prisoners than any other state, is running out of supplies of lethal drugs and may be incapable of carrying out further death sentences beyond June.

The state prides itself on its robust approach to the death penalty, and last year administered the ultimate punishment to 13 death row inmates. The nearest competitor on the league table of judicial killings was Alabama, with six.

Yet Texas has only sufficient quantities in its stores of pentobarbital – the middle drug of the triple lethal injection – to serve in six more executions. That number of executions are scheduled to take place on the state's books over the next four months.

The dwindling supplies in the nation's most prolific death penalty state underline the crisis that is sweeping the 34 states that still have the death sentence on their books. Last summer, Lundbeck, the Danish company that makes pentobarbital under the trademark Nembutal, placed strict restrictions on its distribution to prevent it falling into the hands of US executioners.

Georgia, the state that caused outrage in September when it put to death Troy Davis despite considerable doubts about his guilt, is also running low on stocks of the drug it used to kill him. It has only enough pentobarbital to kill four more prisoners – the same number of executions as it carried out in 2011.

The severity of America's lethal injection drought has been uncovered by the human rights group Reprieve. Using freedom of information appeals, its investigator Maya Foa has calculated the remaining stocks in Texas and Georgia of pentobarbital, a barbiturate used to put prisoners to sleep before they are administered a separate drug to stop their heart.

Her calculations show that Texas has 27 vials of Nembutal left in its stocks, with each vial containing 2.5g of the sedative. The state needs two vials to inject into each condemned prisoner, and a further two as a back-up in case of problems with the first, as outlined in its official execution procedures.

That is sufficient for 6.75 executions.

The Texas Department of Criminal Justice declined to confirm how much pentobarbital it had in its stores, saying it was seeking to keep the quantity secret "for security reasons".

Similarly, Georgia has 17 vials of pentobarbital left, Reprieve has calculated – just over four executions' worth.

"These shows that the restrictions on sale of medical drugs to US corrections departments are starting to bite. States that practice the death penalty are now reaching a desperate situation," Foa said.

"It's getting harder and harder for them to get hold of these drugs and eventually they will be forced to recognise that medicines should not be used to execute people."

Difficulties over lethal injections has already put a halt to executions in several other states. California has a moratorium in place until at least 2013 as a result of legal wrangling over the procedure, while Ohio has also been forced to put its executions on hold because it was found by the courts to be straying from its own protocols in administering the drugs.

The question hanging over death rows across the country is what happens when states like Texas run dry of pentobarbital. Will they move on to a new alternative sedative in the hope of bypassing restrictions on sales of the medicines, or will they try to procure Nembutal through circuitous routes?

Legitimate channels through which the drug can be obtained are fast closing. A ban has been imposed since last December across the European Union on selling the constituent parts of the lethal injection to US prisons.

The next execution in Texas is scheduled for 28 February, when Anthony Bartee is set to die for murdering a 37-year-old man in 1996. Rick Perry, who has presided over 238 executions since becoming governor of the state, wore that record as a badge of pride during his presidential run for the Republican nomination, telling a cheering debate audience that he had never struggled to sleep at night by the idea that anyone might have been innocent.